Was Chicken Run inspired by any specific movies? If so, which?

Specific film references

Nick Park at BBC.co.uk

I don't know. We put some in. Many people have made lists of them. They're there if you spot them and they're not that important. Some people credit us with more than there are. The whole movie started from a joke, a spoof, on the "Great Escape", which is the obvious one, of course. We watched a lot of escape movies. One was"The Flight of the Phoenix" ^*. When Fowler says, "I've never flown a plane before" that's a reference from "Flight of the Phoenix".

Bouncing the brussel sprout against the wall was another reference. None of them are meant to be there as a big joke.

^{* - Not a POW movie though}

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A specific true life incident...sort of.

The eventual plan is to escape captivity via an airplane and this has a direct correspodence to the "Colditz Cock".

Believe it or not, the Colditz Cock was a glider built by British prisoners of war for an escape attempt from Oflag IV-C (Colditz Castle) in Germany.

Wikipedia

Following the execution of 50 prisoners who had taken part in the "Great Escape" from Stalag Luft III, the Allied High Command had discouraged escape attempts, though the plan to build a glider was encouraged in order to divert the energies of the prisoners from descending into boredom and tedium. The idea for the glider came from Lieutenant Tony Rolt. Rolt, who was not even an airman, had noticed the chapel roof line was completely obscured from German view. He realised that the roof would make a perfect launching point from which the glider could fly across the River Mulde, which was about 60 metres below.

The take-off was scheduled for the spring of 1945 during an air raid blackout but by then the Allied guns could be heard and the war's outcome was fairly certain. The British escape officer decided that the glider should be available for use in case the SS ordered the massacre of the prisoners as a way to get a message out to approaching American troops. The glider was approaching completion when the American Army liberated the camp on 16 April 1945.

Although the Colditz Cock never flew in real life, the concept was fictionalized, depicting a successful flight and escape, in the 1971 TV film The Birdmen starring Doug McClure, Chuck Connors, Rene Auberjonois and Richard Basehart.

One episode of the BBC TV series Colditz depicts the decision to build a glider as an escape attempt. It is also depicted in the final escape from Colditz Castle in the fictional story depicted in Prisoner of War, a video game released in 2002.